A Test Of The Capital Asset Pricing Model: Studying Stocks On The Stockholm Stock Exchange

Transcription

1 Mälardalen s University Institution for Mathematics and Physics Västerås, Sweden Bachelor Thesis In Economics A Test Of The Capital Asset Pricing Model: Studying Stocks On The Stockholm Stock Exchange Supervisor: Johan Linden By: Sylvester Jarlee

2 Abstract Date: Level: Author: Tutor: Title: Problem: Purpose: Method: Result: C Thesis In Economics (10 points / 15 ECTS Credit) Sylvester Jarlee Papegojvägen Västerås +46(0) Johan Linden An Empirical Test Of The Capital Asset Pricing Model: Studying Stocks On The Stockholm Stock Exchange Since the birth of the Capital Asset Pricing Model (CAPM), enormous efforts have been devoted to studies evaluating the validity of this model, a unique breakthrough and valuable contribution to the world of financial economics. Some empirical studies conducted, have appeared to be in harmony with the principles of CAPM while others contradict the model. These differences in previously conducted studies serve as a major stimulating factor to my curiosity, the validity of the CAPM. The aim of this paper is to study if the CAPM holds on the Stockholm Stock Exchange, meaning: 1. If higher beta yields higher expected return 2. If the intercept equals zero/average risk-free rate and slope of SML equals the average risk premium and 3. If there exist linearity between the stock beta and the expected return For this research, monthly stock returns for twenty (28) firms listed on the Stockholm Stock Exchange are used. The data ranges from January 2001 to December 2006, a period of six years. To test the CAPM in this paper, I will used approach methods as described by Black, Jensen and Scholes (1972) time-series test as well as Fama and MacBeth (1973) cross-sectional test. It turns out that each of the investigation conducted is a confirmation of the other that the empirical investigations carried out during this study do not fully hold up with CAPM. The data did not provide evidence that higher beta yields higher return while the slope of the security market line is negative and downwards sloping. The data also provide a difference between average riskfree rate, risk premium and their estimated values. However, a linear relationship between beta and return is established. To an extend, the consequence of the tests conducted on the data with period to obtained from the Stockholm Stock Exchange do not appear to absolutely reject CAPM. On the other hand, I cannot say that the data do not support CAPM since there are other factors available and capable of affecting the results. 2

3 Acknowledgement I would like to thank 3

4 Table of Contents 1. Introduction Brief Presentation of CAPM Brief Presentation of Stockholm Stock Exchange Problems Purpose Organizational Structure Theoretical Framework The Theory of CAPM Implications of the Theory Assumptions of the Theory Evidence of the Theory The Black-Jensen-Scholes Study (1972) The Fama and MacBeth Study (1973) Challenges to the Theory APT- An Alternative Relating APT to the CAPM Empirical Method Sample Selection Data selection Testing Methods Portfolio Formation Period Initial Estimation Period Testing Period Significance Testing Results and Analysis First Results Portfolio Formation Initial Estimation Testing Second Result Testing Conclusions Conclusion Result From The First Investigation Result From The Second Investigation Future Research References Literatures Journals Internet Sources Method: Least Squares... Error! Bookmark not defined. 4

5 1. Introduction Since the birth of the Capital Asset Pricing Model (CAPM), enormous efforts have been devoted to studies evaluating the validity of this model, a unique breakthrough and valuable contribution to the world of financial economics. Some empirical studies conducted, have appeared to be in harmony with the principles of CAPM while others contradict the model. These differences in previously conducted studies serve as a major stimulating factor to my curiosity. Being a student, it is a privilege using this paper particularly, to deeply enhance the principles of CAPM and evaluate the validity of the model using stocks from the Stockholm Stock Exchange. 1.1 Brief Presentation of CAPM One of the significant contributions to the theory of financial economics occurred during the 1960s, when a number of researchers, among whom William Sharpe was the leading figure, used Markowitz s portfolio theory as a basis for developing a theory of price formation for financial assets, the so-called Capital Asset Pricing Model (CAPM). Markowitz s portfolio theory analyses how wealth can be optimally invested in assets, which differ in regard to their expected return and risk, and thereby also how risks can be reduced. For his contribution of this model, CAPM, William F. Sharpe was awarded together with Harry Markowitz and Merton Miller the 1990 Alfred Nobel Memorial price in economic sciences with one third. The foundation of the CAPM is that an investor can choose to expose himself to a considerable amount of risk through a combination of lending-borrowing and a correctly composed portfolio of risky securities. The model emphasizes that the composition of this optimal risk portfolio depends entirely on the investor s evaluation of the future prospects of different securities, and not on the investors own attitudes towards risk. The latter is reflected exclusively in the choice of a combination of a risky portfolio and risk-free investment or borrowing. In the case of an investor who does not have any special information, that is better information than other investors, there is no reason to hold a different portfolio of shares than other investors, which can be described as the market portfolio of shares. The Capital Asset Pricing Model (CAPM) incorporates a factor that is known as the beta value of a share. The beta of a share designates its marginal contribution to the risk of the entire market portfolio of risky securities. This implies that shares designated with high beta coefficient above 1 is expected to have over-average effect on the risk of the total portfolio while shares with a low beta coefficient less than 1 is expected to have an under-average effect on the aggregate portfolio. In efficient market according to CAPM, the risk premium and the expected return on an asset will vary in direct proportion to the beta value. The equilibrium price formation on efficient capital market generates these relations. The model is considered as the backbone of contemporary price theory for financial markets and it also widely used in empirical investigations, so that the abundance of financial statistical data can be utilized systematically and efficiently [1]. 1 1 See reference [10] 5

6 1.2 Brief Presentation of Stockholm Stock Exchange The author of this paper deemed it necessary to provide its readers with a brief information about the stockholm stock exchange since it is/will be of necessity to the data used in the empirical study and the entire paper as a whole. The Stockholm Stock Exchange is a stock exchange located in Stockholm, Sweden. It was founded in 1863 and is the primary securities exchange of the Nordic Countries, which was acquired by OMX [2] in In 2003, the operations were merged with those of the Helsinki Stock Exchange and prior to the introduction of electronic trading on 1 June 1990, all trading was conducted on the floor of the Stockholm Exchange Building. The Stocholm Stock Exchange also termed as the Nordic Exchange serves as a central gateway to the Nordic and Baltic financial markets, promoting greater interest, opportunity and investment in the whole region. Securities listed on the stock exchange are in the form of stocks, bonds, options, futures, warrants and funds. By the year 2004, the numbers of firms listed were about 310 with a market capitalization value of trillion Swedish kronor [3]. 1.3 Problems Since the birth of the Capital Asset Pricing Model (CAPM), enormous efforts have been devoted to studies evaluating the validity of this model, a unique breakthrough and valuable contribution to the world of financial economics. Some empirical studies conducted, have appeared to be in harmony with the principles of CAPM while others contradict the model. These differences in previously conducted studies serve as a major stimulating factor to my curiosity, the validity of the CAPM in application with historical data collected from the Stockholm Stock Exchange. 1.4 Purpose The aim of this paper is to study if the CAPM holds on the Stockholm Stock Exchange, meaning: 1. If higher beta yields higher expected return 2. If the intercept equals zero/average risk-free rate and slope of SML equals the average risk premium and 3. If there exist linearity between the stock beta and the expected return 1.5 Organizational Structure The paper is organized in six (6) sections. Section one (1) is the introductory section of the paper. It highlights the purpose of the research, brief background, basis of the CAPM and presents an organizational structure of the entire paper. Section two (2) illustrates an indept theoretical framework of the model, support/strenght and challenges/weakness of the model. It also includes a brief discription of the Arbitrage Pricing Theory (APT) and the relationship of this theory to the CAPM. Section three (3) introduces the testing methods, outsourcing of data and application of data to methods to conduct empirical study. Section (4) contains results and findings from the empirical study. Section (5) also contains conclusion and interest of future research. The last section, References contains sources used to produce this paper. The references are categorized in the form of literature, journals and Internet. 2 See figure one. 2 See reference [10] 6

7 Figure One 3 See reference [11] 7

8 2. Theoretical Framework This section of the paper is considered one of the most important parts. It contains illustrative and indept theoretical framework. Substaintial evidences favouring the model are presented as well as contra evidences. It also includes a brief discription of the Arbitrage Pricing Theory (APT) and a comparison of this theory to the CAPM. The context of this section seeks simplicity intented to suit persons with little or no previous knowledge on the Capital Asset Pricing Model (CAPM). 2.1 The Theory of CAPM The Capital Asset Pricing Model often expressed as CAPM of William Sharpe 3 (1964) and John Litner 4 (1965) points the birth of asset pricing theory. It describes the relationship between risk and expected return and is used in the pricing of risky securities. The CAPM is still widely used in evaluating the performance of managed portfolio and estimating the cost of capital for firms even though, it is about four and a half decades old. The Capital Asset Pricing Model, CAPM emphasizes that to calculate the expected return of a security, two important things needs to be known by the investors: The risk premium of the overall equity/portfolio (assuming that the security is only risky asset) The security s beta versus the market. The security s premium is determined by the component of its return that is perfectly correlated 5 with the market, meaning the extent to which the security is a substitute for investing in the market. In other word, the component of the security s return that is uncorrelated with the market can be diversified away and does not demand a risk premium. The CAPM model states that the return to investors has to be equal to: The risk-free rate Plus a premium for the stocks as a whole that is higher than the risk-free rate. Multiplied by the risk factor for the individual company. This can be expressed mathematically as E[R i ] = R f + β i (E[R m ] R f ) 1 Where E[R i ] R f β i E[R m ] E[R m ] R f = Expected Return = Risk-free rate = Beta of the security i = Expected Return on the market = Market premium 3 Sharpe, W.F. (1964) Capital Asset Prices: A theory of market Equilibrium under Condition of Risk. Journal of finance.19: Lintner, J (1965) Security Prices, Risk and Maximal Gains from Diversification. Journal of Finance. 20: Perfectly correlated means that the stock and the portfolio excess returns move together in a fixed ratio plus a constant. The fixed ratio is called beta, β and the constant is alpha, α. 8

9 Equation one (1) shows that the expected return on security i is a linear combination of the risk-free return and the return on portfolio M. This relationship is a consequence of efficient set mathematics. The coefficient Beta, β measures the risk of security i, and is related to the covariance of security i with the tangency portfolio, M. Therefore, as mentioned earlier, the expected return will equal the risk-free asset plus a risk premium, where the risk premium depends on the risk of the security. The equation describing the expected return for security i is referred to as the security market line (SML). In the SML equation, expected returns are linear and the coefficient beta is: β i = σ im / σ 2 m 2 The security market line, SML is sometimes called the Capital Asset Pricing Model (CAPM) equation. It states the relationships that must be satisfied among the security s return, the security s beta and the return from portfolio M. The CAPM model introduces simple mechanism for investors and corporate managers to evaluate their investments. The model indicates that all investors and managers need to do is an evaluation and comparison between expected return and required return. If the expected result is otherwise unfovourable, it is necessary to abort intentions for potential investment in the particular security Implications of the Theory The CAPM is associated with a set of important implications which are often the basis for establishing the validity of the model. They are as follows: Investors calculating the required rate of return of a share will only consider systematic risk 6 to be relevant. Share that exhibit high levels of systematic risk are expected to yield a higher rate of return. On average there is a linear relationship between systematic risk and return, securities that are correctly priced should plot on the SML Assumptions of the Theory The CAPM is associated with key assumptions that represent a highly simplified and natural world. Given sufficient complexities, to understand the real world and construct models, it is necessary to assume away those complexities that are thought to have only a little or no effect the its behaviour. Generally it is accepted that the validity of a theory depends on the empirical accuracy of its predictions rather than on the realism of its assumptions. The major assumptions 7 of the CAPM are: All investors aim to maximize the utility they expect to enjoy from wealthholding. All investors operate on a commmon single-period planinig horizon. 6 In a financial context, risk is comprise of systematic risk and non-systematic risk. Systematic risk is any risk that affects a large number of assets, each to a greater or lesser degree while non-systematic is any risk that affects a single asset without impact on the all assets. 7 See reference [5] 9

10 All investors select from alternative investment opportunities by looking at expected return and risk. All investors are rational and risk-averse. All investors arrive at similar assessments of the probability distributions of returns expected from traded securities. All such distributions of expected returns are normal. All investors can lend or borrow unlimited amounts at a similar common rate of interest. There are no transaction costs entailed in trading securities. Dividends and capital gains are taxed at the same rates. All investors are price takers: that is, no investor can influence the market price by the scale of his or her own transactions. All securiteies are highly divisible, i.e. can be traded in small parcels Evidence of the Theory It was earlier stated in this paper that considerable research has been conducted to test the validity of the CAPM. Some of these findings provide evidence in support of the Capital Asset Pricing Model while others present evidence raising questions about the validity of the model. Among other test providing evidence of the model are two classic studies, Black, Jensen & Scholes 8 and Fama & MacBeth The Black-Jensen-Scholes Study (1972) In their studies, Black, Jensen & Scholes use the equally-weighted portfolio of all stocks traded on the New York Stock Exchange (NYSE) as their proxy for the market portfolio. They calculated the relationship between the average monthly return on the portfolios and the betas of the portfolios between 1926 and 1966, a period of forthy years. The findings from their study provided a remarkable tight relationship between beta and the monthly return as shown visually in figure two 10. Figure Two Monthly Returns as a Function of β 8 Black, F., Jensen, M.C. and Scholes, M. (1972) The Capital Asset Pricing Model: Some empirical tests. Studies in the Theory of Capital Markets. New York: Praeger. 9 Fama, E.F. and MacBeth, J. (1973) Risk, return and equilibrium: Empirical tests. Journal of Political Economy

11 Given the result from their study, Black, Jenson & Scholes did not reject the linearity predicted by CAPM because there exist a positive linear relationship between average return and beta, although the intercept appears to be significantly different and greater then the average risk-free rate of return over the period studied The Fama and MacBeth Study (1973) 11 The next classical test to be discussed in support of the CAPM is the study conducted by Fama & MacBeth (1973). They evaluated stocks traded on NYSE with similar period as that of Black, Jensen & Scholes study. They also took as their proxy for the market portfolio an equally weighted portfolio of all NYSE stocks and focused on two implications of CAPM; Linearity between the expected return and the beta of a portfolio. Expected return being determined purely by a portfolio s beta and not by the residual variance or non-systematic risk of the portfolio. They regressed the result after estimating betas and historical average returns and obtained the following regressions: r p = α 0 + α 1 β p + α 2 β 2 + ε p r p = α 0 + α 1 β p + α 2 β 2 + α 0 RV p + ε p Given, RV p = N 2 σ i=1 N ( ε ) i 3 Where N = number of stocks P = portfolio RV = Average of residual variance The logic of the test is that, given the SML equation holds as predicted by CAPM then, α 0 should be equivalent to the average risk-free interest rate, α 1 should be equivalent to the excess return on the market and α 2 and α 3 should be equivalent to zero. Fama & MacBeth performed a significance test and concluded that α 2 and α 3 were not significantly different from zero which serves as an evidence and support to the CAPM theory. 11 See reference [7] and [17] 11

12 2.3 Challenges to the Theory Even though, the CAPM is still applied in financial institutions and taught in schools around the globe, it is indeed a subject to criticism. Researchers around the world question the application of the Capital Asset Pricing Model as a result of empirical studies conducted. Fama and French present some of the most famous contradictions. Fama and French (1992) present evidence on the empirical failures of the CAPM. In their study, portfolio group formation of similar size and betas from all non-financial stocks traded on the NYSE, NASDAQ 12 and AMEX between 1963 and 1990 are taken into consideration. Fama and French used the same approach as Fama and MacBeth (1973) but arrived at very different conclusion, no relation at all. Fama and French (1996) reach the same conclusion using the time-series regression approach applied to portfolios of stocks sorted on price ratios and find that different price ratios have much the same information about expected returns 13. In short, Fama and French concluded that firm size and other accounting ratios are better predictors of observed returns than beta. Richard Roll 14, often referred to as the Roll s Critique presented another challenge that surfaced in Roll (1977) criticized all efforts to test the Capital Asset Pricing Model. The basis of the Roll s Critique is the efficiency of the market portfolio s implication in CAPM. The market portfolios by theory include all types of assets that are held by anyone as an investment. In application, such a market portfolio is unobservable and people usually substitute a stock index as a proxy for the true market portfolio. Roll argue that such substitution is not innocuous and can lead to false inferences as to the validity of the CAPM and due to the lack of ability to observe the true market portfolio, the CAPM might not be empirically testable. In a nutshell, tests must include all assets available to investors APT- An Alternative The arbitrage pricing theory (APT) has been proposed as an alternative to the capital asset pricing model (CAPM). It is a new and different approach to determine asset prices and centres around the law of single price: similar items cannot sell at different prices. The theory was initiated by the economist Stephen Ross in APT states that the expected return of an asset can be modelled as a linear function of various macro-economic factors 15 or theoretical market indices, where a factor s specific beta coefficient represents the sensitivity of changes in each factor. The model obtained rate of return will then be used to price the asset accurately, having the asset price equal to the expected end of period price discounted at the rate implied by the model. In such case, if the price diverges, arbitrage is expected to bring it back into line NASDAQ (originally an acronym for National Association of Securities Dealers Automated Quotations system) is an American electronic stock market. 13 See reference [9b] 14 See reference [9c] 15 Chen, Roll, and Ross (1986) refer to the factors as level of productivity in the country, inflationary expectations, the spread between the short and long end of the default free yield curve and the spread between low and high default rates on risky debt. 16 See reference[19a] 12

13 The model is associated with a couple of assumptions and requirements that are established in an attempt to get rid of impurities in the latter. The assumptions are that: Security returns are generated by a multi-factor model The return generating process model is linear Additionally, it is required that there must be perfect competition in the market, and the total number of factors may never surpass the total number of assets. The equation representing this model is as follows; r i = β 0 + β ia F A + β ib F B + + β ik F K + ε i Where r i = the rate of return on security i, a random variable; β 0 = the expected level of return for the stock i if all indices have a value of zero. β ik = the ith security's return responsiveness to factor k; F A = non-diversifiable factor A; F B = non-diversifiable factor B, and so on; = the idiosyncratic risk or residual term, which is independent across securities. ε i In order for the model to fully describe the process generating security returns, E (e i e K ) = 0 E [e i (F K - F K )] for all i and k where i is not equal to j and for all stocks and indexes 2.5 Relating APT to the CAPM The APT along with the CAPM are two influential theories on asset pricing. The APT differs from the CAPM in a sense that it is less restrictive in its assumption. It allows for an explanatory model of asset returns. Furthermore, it assumes that each investor will hold a unique portfolio with its own particular array of betas, as opposed to the identical market portfolio. 17 The interpretation of the factor introduces the major difference between the two models. For CAPM, the factor is the market index M (the value-weighted index of all risky securities) while for the APT, this could be M, but is not restricted to M. For instance, the factor could be a proxy for M. That is, APT still makes a prediction given some proxy for M something that CAPM connot provide. In both cases, there is a simple linear relationship between expected excess returns and the security s beta 18. In some ways, the CAPM can be considered a special case of the APT in that the security market line represents a single-factor model of the asset price, where beta is exposure to changes in the market. 17 See reference [19a] 18 See reference [19b] 13

14 3. Empirical Method This section presents the testing methods of the CAPM which are later used to obtain results for further analysis. Given the procedures, data are outsourced and applied to methods to conduct studies. 3.1 Sample Selection The data used of this study covers the period of six (6 ) years, from to This period was select as a result of unavailable historical data for some of the stocks as well as the market index. Initially, the thirty (30) most traded stocks on the Stockholm Stock Exchange with a period of ten (10) years was a focus of this study. In order to maintain a longer time frame and maximum number of firms, six years was chosen and two firms were omitted because they did not meet my periodic requirements. The stocks used are comprised as A and B stock. 3.2 Data selection During this study, I am using monthly stocks returns from companies listed on the Stockholm Stock Exchange for the period of six (6) years. The stocks are the most traded on the stocks and their data were obtained from the Stockholm Stock Exchange s (omx) official webpage in the form of daily prices. In the studies conducted by Black et al (1972), average monthly data are used while during this study, I choose to use the last day closing prices of the month to represent monthly data and OMXSI30 as the proxy of the market index. This is because the index was established for the A and B shares listed on the Stockholm Stock Exchange. It is a valued weighted index comprising of 30 most traded stocks and reflects the trend of the market. Also, the existing monthly Swedish treasury bill is used as a proxy for the risk-free rate. The yields were obtained from the Swedish Statistic Bureau s homepage and are expected to reflect the shortterm changes on the Swedish financial market. All stocks returns used for the purpose of this paper are not adjusted for dividends. However, the results are not expected to be greatly affected by such unadjustments since earlier researchers, including Black et al (1972) have applied similar measures. 3.3 Testing Methods To test the CAPM for the Stockholm Stock Exchange, a six year period is used as well as methods introduced by Black et. al (1972) and Fema-MacBeth (1973). Considering the short observation period, the investigation is dividual into three main periods. These periods are the portfolio formation period, estimation period, and testing period Portfolio Formation Period The portfolio formation period is the first step of the test. During this period, Black et. al(1970) used a time series test o the CAPM to regress excess return on excess market return. Similary, I am using this period to estimate beta coefficient for individual stocks using 14

15 monthly returns for the period to The betas estimation is conducted by regression using the following time series formula: R it R ft = a i + β i (R mt R ft ) + e it 5 Where R it = rate of return on stock i (i = ) R ft = risk free rate at time t β i = estimate of beta for stock i R mt = rate of return on the market index at time t e it = random disturbance term in the regression equation at time t The above equation, five (5) is also expressible as r it = a i + β i.r mt +e it 6 Where r it = R it R ft = excess return of stock i (i = ) r mt = R mt R ft = average risk premium. a i = the intercept. The intercept a i is supposed to be the difference between estimated return produced by time series and the expected return predicted by CAPM. The intercept a i of a stock is zero equivilent if CAPM s description of expected return is accurate. The individual stock s beta once obtained after series of estimation are used to create equally weighted average portfolios. The equally weighted average portfolios are created according to high-low beta criteria. Portfolio one contains a set of securities with the highest betas while the last portfolio contains a set of low beta securities. Organizing and grouping securities into portfolios 19 is considered a strategy of partially diversifying away a portion of risk whereby increasing the chances of a better estimation of beta and expected return of the portfolio containing the securities Initial Estimation Period Within this estimation period, regression is run using the beta information obtained from the previous period. The purpose of this period is to estimate individual portfolio betas. Fama- MacBeth applied crossed-sectional regression on its data and regress average excess return 21 on market beta of portfolios. The formula used to calculate portfolios beta is r pt = a p + β p.r mt + e pt 7 Where r p = average excess portfolio return 19 In this paper, twenty eight securities are used to form different numbers of portfolios. At a stage, three portfolios where formed having the first and second to contain 10 securities each and the last 8 securities. 20 See reference [2] 21 Average excess return is calculated as the total access return of the portfolio divided by the number of securities in the portfolio during a period. 15

16 β p = portfolio beta When the regression result is obtained, the data is used to investigate if high beta yields high returns and vice versa Testing Period After estimating the portfolios betas in the previous period, the next step is estimating the expost Security Market Line (SML) by regressing the portfolio returns against portfolio betas. To estimate the ex-post Security Market Line, the following equation is examined: r p = γ 0 + γ 1 β p + e p 8 Where r p = average excess portfolio return β p = estimate of beta portfolio p γ 0 = zero-beta rate γ 1 = market price of risk and e p = random disturbance term in the regression equation The hypothesis presented by CAPM is that the values of γ 0 and γ 1 after regression should respectively be equivalent to zero and market price of risk, the average risk premium. Finally, the test for non-linearity is conducted between total portfolio returns and portfolio beta. The equation used is similar to equation eight (8) but this time, a beta square factor is added to the equation as shown below: r p = γ 0 + γ 1 B p + γ 2 B p 2 + e p 9 To provide an evidence for CAPM, γ 2 should equal zero and γ 0 should equal average risk free rate. The value of γ 1 could be negative but different from zero Significance Testing To evaluate the data and regression result available within the testing period, I will conduct as a statistical test referred to as significance testing. It is the test of important null hypothesis, which states that the independent variable has no effect upon the dependent variable 22. The test is often conducted using P-values or t-values. For the purpose of this paper, I choose the t- values criteria since it is easier in application. I am also using null hypothesis in referring to H 0 : X = 0 and alternative hypothesis in referring to H a : X 0 where will be the coefficient under investigation. Basically, a significance test is conducted to determine if the coefficients are significantly different from zero. In defining the data significant to conclude with 95% confidence, I selected a 5% level of significance. The critical value t c is 2,056 for a t-distribution with 26 degrees of freedom. However, the rejection region for the null hypothesis becomes / t / 2,056. This means that I will reject the null hypothesis, in favour of the alternative, if / t / 2, Undergraduate Econometric ad,,,,,,,,, 16

17 4. Results and Analysis During this part, results obtained from the application of the empirical methods discussed in the previous chapter are presented. The methods are the basis for the test of CAPM. Equally, analysis of the results obtained will be made within this section. To strengthen the reliability of the results, two types of investigation was carried out. I am firstly presenting results of the investigation conducted with data under the entire period from to using diversification through portfolio formation. The second investigation also contains data of the entire period from to but is not subject to diversification through portfolio formation. 4.1 First Results Portfolio Formation At this initial stage, beta values of the individual stocks are estimated using equation (5). A detailed table containing stocks, betas and their average access returns is included in appendix 1A. For now, a diagram is presented below in figure (3) to give a view of the stocks betas. Stocks' Betas Estimate 3 2,5 2 Beta 1,5 1 0,5 0-0,5 ERICRF NOKIRF TELERF INVERF VOLVORF ELUXRF SCVRF SECURF HMRF Stocks TSLNRF ENIRORF SANDRF SHBRF AZNRF Figure Three. A plot of the stocks estimated beta (self-made) 17

18 4.1.2 Initial Estimation With a condition that the relationship between stocks and betas is established, the next stage is to form portfolios using the sizes of the individual betas. Using this information, six portfolio were formed and regressed using equation (7). The individual portfolio beta estimate along with its average access return is given in table one (1). Portfolio Nr. Portfolio Beta Average Excess Returns 1 1, , , , , , Table one. Portfolio Beta Estimates The result in table one (1) containing portfolio betas and their average excess returns, presents the nature of high beta/ high return and low beta/low return criteria described by the CAPM. The characteristics of the result do not provide support of the hypothesis. That is, portfolio one with the highest beta does not have a high return in comparison to portfolio four, which has a lower beta but is associated with the highest return amongst all the portfolios. To support the theory, returns on portfolios should match their betas. A plot is also presented in figure two (4) below. Portfolio Beta Estimate Beta 2,5 2 1,5 1 0, Portfolio Figure Four. Portfolio Beta Estimates 18

19 4.1.3 Testing Since I know the values of the portfolio betas, I estimated the SML coefficients using equation (8). The result is sumarized in the table below; Coefficients Std. Error t-statistic Probability γ γ Table (2). Statistics for SML Estimation. The hypothesis presented by CAPM is that the values of γ 0 and γ 1 after regression should respectively be equivalent to zero and market price of risk, the average risk premium. To see this, I conduct a significance test. According to CAPM, γ 0 should be zero. As mentioned earlier, using a null hypothesis that the intercept γ 0 is zero, I reject this hypothesis since the t-value is larger than 2,056. This actually means that the coefficient is significantly different from zero, which is a contradiction to the theory of CAPM. Conducting a test for the second coefficient γ 1 indicates that the value of the coefficient is significantly different from zero since its absolute t-value is larger than 2,056. Comparing the value of the slope to the average excess return on the market portfolio or the average risk premium, it is an advantage that is not equal to zero but what similarity lies between the estimated value and the calculated value? The calculated value is 0,00202 while the estimated value is 0,126779, which appears to be a contradiction to CAPM. The graphical relationship of the SML is estimated using regressions in Eviews and is presented below; Figure Five (5): SML Estimation (Average Access Portfolio Return Vs Portfolio Beta) 19

20 The last step is to test for non-linearity between average excess portfolio returns and betas. To do this, equation (9) is used in regression using a beta square factor. The result is summarized below; Coefficients Std. Error t-statistic Probability γ γ γ Table (3) Statistics for Non-Linearity Test To provide an evidence for CAPM, γ 2 should equal zero and γ 0 should equal average risk free rate. The value of γ 1 must equal the average risk premium. The nature of γ 2 shall determine the linearity condition between risk and return. The test indicates that the value of the intercept γ 0 is not significantly different from zero since its t-value is smaller than 2,056. However, this value is not equal to the average risk free rate, 0, and is an evidence against CAPM. Though the coefficient of γ 1 is negative, the test indicates that it is also not significantly different from zero since its absolute t-value is smaller than 2,056. As well, the coefficient is not equal to the average market premium as described by CAPM. The test conducted for γ2 indicates that the coefficient is not significantly different from zero and provides an evidence for CAPM. Well, having the coefficient not significantly different from zero signifies that the expected rate of returns and betas are linearly related to each other. 20

21 4.2 Second Result It was mentioned earlier in the beginning of this section that this second investigation will disregard the usage of portfolio diversification method to observe what different would surface in the result with comparison to the first investigation of this paper. By so doing, I am proceeding directly to the testing since I am not forming portfolios to estimate their betas. Similar stocks betas estimated in the earlier investigation are used to estimate the security market line for all twenty-eight (28) stocks or securities Testing Given the stocks beta estimates in figure one (1) and in appendix one (1), table A, I run regression using equation eight (8) to estimate the SML and obtained the following results; Coefficients Std. Error t-statistic Probability γ 0 0, , , ,0185 γ 1-0, , , ,2552 Table (4). Statistics for SML Estimation. Again, hypothesis presented by CAPM is that the values of γ 0 and γ 1 after regression should respectively be equivalent to zero and market price of risk, the average risk premium. To see this, I use a significance test. According to CAPM, γ 0 should be zero. As mentioned earlier, using a null hypothesis that the intercept γ 0 is zero, I reject this hypothesis since the t-value is larger than 2,056. This actually means that the coefficient is significantly different from zero, which is a contradiction to the theory of CAPM. Conducting a test for the second coefficient γ 1 indicates that the value of the coefficient is not significantly different from zero since its absolute t-value is smaller than 2,056. Comparing the value of the slope to the average excess return on the market or the average risk premium, the calculated value is 0,00202 while the estimated value is 0,360325, which appears to be a contradiction to CAPM. A graphical relationship of the SML is estimated using regressions in Eviews and is presented below; Figure Six (6): SML (Average Access Stock Return Vs Stock Beta) 21

22 For this section, the last step is to test for non-linearity between average excess stock returns and betas. To do this, equation (9) is used in regression using a beta square factor. The result is summarized below; Coefficients Std. Error t-statistic Probability γ γ γ Table (5) Statistics for Non-Linearity Test If CAPM is to be supported, γ 2 should equal zero and γ 0 should equal average risk free rate. The value of γ 1 must equal the average risk premium. The nature of γ 2 shall determine the linearity condition between risk and return. The test indicates that the value of the intercept γ 0 is not significantly different from zero since its t-value is smaller than 2,056. However, this value is not equal to the average risk free rate, 0, and is an evidence against CAPM. For the coefficient of γ 1, the test indicates that it is not significantly different from zero since its absolute t-value is smaller than 2,056. As well, the coefficient is not equal to the average market premium as described by CAPM. The test conducted for γ 2 indicates that the coefficient is not significantly different from zero and provides an evidence for CAPM. Well, having the coefficient not significantly different from zero signifies that the expected rate of returns and betas are linearly related to each other. 22

23 5. Conclusions This section of the paper contains summary of findings obtained from the analysis. These findings are the basis for conclusion on how well CAPM responds to the data used in the investigation. At a later part, I am presenting an area of interest for further research purposes. 5.1 Conclusion This study has been established to investigate the validity of CAPM on Stockholm Stock Exchange. It uses monthly stock returns from 28 firms listed on the Stockholm Stock Exchange ranging from to The stocks used in the study are considered the most traded on the Swedish financial market. Methods used to evaluate the model are similar to those introduced by Black et. al (1972) and Fama-MacBeth (1973), which are the time series and cross-sectional approaches. These methods were used as an aid to achieve the purpose of this paper. The purpose of this paper has been to examine whether the model, CAPM holds truly on the Stockholm Stock Exchange by testing: 1. If higher beta yields higher expected return 2. If the intercept equals zero and slope of SML equals the average risk premium 3. If there exist linearity between the stock beta and the expected return To examine this, the data were handled in two different ways to assess if there might be a considerable difference in the investigation methods. The Findings are summarized below: Result From The First Investigation 1. Using portfolio formation to diversify away most of the firm-specific part of risk thereby enhancing the beta estimates, the findings from the first investigation appears inconsistent with the theory s basic hypothesis that higher beta yields higher return and vice versa. 2. The CAPM model implies that the prediction for the intercept be zero and the slope of SML equals the average risk premium. The findings from the test are also inconsistent with Theory of CAPM, indicating evidence against the model. 3. The hypothesis and implications of CAPM predicts that there exist a linear relationship between expected return and beta. It occurred that the findings from the test are consistent with the implications and provide evidence in favour of CAPM Result From The Second Investigation 1. Using stocks beta estimates without portfolio formation, the findings from the second investigation still appear inconsistent with the theory s basic hypothesis that higher beta yields higher return and vice versa. 23

24 2. The CAPM model implies that the prediction for the intercept be zero and the slope of SML equals the average risk premium. Similarly, the findings from the test are also inconsistent with Theory of CAPM, indicating evidence against the model. 3. The hypothesis and implications of CAPM predicts that there exist a linear relationship between expected return and beta. It occurred that the findings from the test are also consistent with the implications and provide evidence in favour of CAPM. Given the above, it turns out that each of the investigation conducted is a confirmation of the other that the empirical investigation carried out do not fully hold up with CAPM. Well, the consequence of the tests conducted on the data with period to from the Stockholm Stock Exchange do not appear to absolutely reject CAPM. On the other hand, I cannot say that the data do not support CAPM since there are other factors available and capable of affecting the results. Black et.al (1972) describes some of these factors as measurement and model specification errors. These errors, however, arises because of the usage of a proxy and not the real market portfolio and leads to biasing the estimated slope towards zero as well as estimating the intercept away from zero. So far, this investigation has only evaluated CAPM in combination with historical data of stocks obtained from Stockholm Stock Exchange. This study does not present an evidence for any other model even though it may present inconsistency with CAPM. 5.2 Future Research Given the results of my studies, I am not really surprised but a bit disappointed. I had really wished the study provided an evidence for CAPM. On the other hand, other studies including Fama-French (2004), Michailidis et.al (2006) and Yang et.al (2006) provide evidence against the model. My interest and curiosity drove me to select this research topic. At this point, I am even more curious and would like to conduct further research on the same topic, the validity of the CAPM but using a period of ten years with at least 100 securities along with a well selected market index and market portfolio. It will also be of interest to consider alternative models and study the results in relations to CAPM. 24

25 6. References 6.1 Literatures 1.Bernhardsson, Jonas (2002) Tradingguiden: Bokförlaget Fischer & Co. 2.Elton, E.J., Gruber, M.J., Brown, J.S. and Geotzman, W. N. (2003) Modern Portfolio Theory and Investement Analysis. 6 th edition, New Jersey: John Wiley & Sons, Inc. 3.Ross, S.A., Westerfield, R.W. and Jaffe, J. (2005) Corporate Finance. 7 th edition. McGraw- Hall/Irwin. 4.Ross, S. M. (1999) An Introduction To Mathematical Finance: Options and other Topics. United Kingdom: Syndicate of the University of Cambridge 5. Pike, R and Neale Bill (2003) Corporate Finance and Investment. 4 th edition. Pearson Education Limited Journals 5.Black, F., Jensen, M.C. and Scholes, M. (1972) The Capital Asset Pricing Model: Some empirical tests. Studies in the Theory of Capital Markets. New York: Praeger. 6.Black, F. (1993) Beta and return Journal of Portfolio Management Fama, E.F. and MacBeth, J. (1973) Risk, return and equilibrium: Empirical tests. Journal of Political Economy Sharpe, W.F. (1964) Capital Asset Prices: A theory of market Equilibrium under Condition of Risk. Journal of finance. 19: Lintner, J (1965) Security Prices, Risk and Maximal Gains from Diversification. Journal of Finance. 20: Perold, A. F. (2003) The Capital Asset Pricing Model. The Journal of Economic Perspectives. 18 9b. Fama, E.F. and French (2004) The Capital Asset Pricing Model: Theory and Evidence. The Journal of Economic Perspectives.18 9c. Roll, Richard. (1977). A Critique of the Asset Pricing Theory s Tests Part 1: On Past and Potential Testability of the Theory. Journal of Financial Economics. 4:2 pp Internet Sources /04/ /04/ /04/ /04/ /04/ /04/ /04/ /04/ /04/25 19a /04/26 19b /04/26 25

26 APPENDICES APPENDIX I Table 1. Portfolio Formation The individual stocks beta was estimated and six portfolios are formed using this estimates. Portfolio One Nr. Stock Beta Average Excess Return 1 ERICRF ABBRF NOKIRF SKARF TELERF Portfolio Two 6 ASSARF INVERF ATCOBRF VOLVORF ATCOARF Portfolio Three 11 ELUXRF ALIVRF SCVRF NDARF SECURF Portfolio Four 16 SEBRF HMRF VOSTRF TSLNRF SWEDRF Portfolio Five 21 ENIRORF STERRF SANDRF SKFRF Portfolio Six 25 SHBRF SCARF AZNRF SWMARF

27 Table 2. Regression Results for Excess Portfolio Return Verses Excess Market Returns Method: Least Squares Dependent Variable Coefficient Std. Error t-statistic Prob. Variable P1RF INRF C P2RF INRF C P3RF INRF C P4RF INRF C P5RF INRF C P6RF INRF C Table 3. Regression Result for Testing SML Equation Method: Least Squares Dependent Variable Coefficient Std. Error t-statistic Prob. Variable Av. Ace. PB PR C Table 4. Regression Result for Testing for Non-Linearity Method: Least Squares Dependent Variable Coefficient Std. Error t-statistic Prob. Variable Av. Ace. P. PB Return PB^ C